A) Using the phrase "a certain number" when that number is one is a pretty contrived example.

2) That's not a very standard definition of "case". Many linguists don't even admit that case exists in English outside of pronouns, but I don't know anyone who defines "case" as "nouns or pronouns".

Þ) When using such phrases as "a/the number of" or the like one must be very careful to determine whether one is talking about the number or the thing being numbered. "The number of insects on the wall has been increasing over the past few days" vs. "a number of insects have been crawling on the wall over the past few days.

My point is that "case", meaning nouns or pronouns, must agree in number with singular or plurals verbs and in number with the objects of the verb. Simple huh?

Um, that's not what case is. Case is a grammatical category whereby the relationship of nouns to verbs is expressed by inflections (in IE languages suffixes). One kind of grammatical concord is the phenomenon whereby adjectives and nouns agree in case and number. Number is a grammatical category that applies to both nouns and verbs. Another kind of grammatical concord is agreement between the number of the noun or noun phrase that is the subject of a sentence and the verb.

Not all languages treat number in the same manner. In Classical Greek, a plural neuter noun as the subject of a sentence takes the singular form of the verb (in the third person). Feminine and masculine plural subject take the verb in the plural.

When Old English lost its case distinctions (a process that started before the Norman Conquest), it went from being a free-word-order language to one more fixed in its word order. There are remnants of case in the pronominal system in Present Day English.

Grammatical categories such as grammatical gender, number, case, tense, mood, etc., are anything but simple if one studies grammar seriously.

In phrases like "a number of X" or "a lot of Y", the copula in "there is/are" tends to agree with the number of the nouns X or Y. It's as though the fragments "a lot of" and "a number of" are being reanalyzed as quantifiers. With other phrases, the singular verb sounds better: e.g., "there is a cohort of freshmen sleeping in the dormitory hallway" or "there is a hovercraft full of eels outside".

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